Abstract
Propositional satisfiability (SAT) solvers, which typically operate using conjunctive normal form (CNF), have been successfully applied in many domains. However, in some application areas such as circuit verification, bounded model checking, and logical cryptanalysis, instances can have many parity (xor) constraints which may not be handled efficiently if translated to CNF. Thus, extensions to the CNF-driven search with various parity reasoning engines ranging from equivalence reasoning to incremental Gaussian elimination have been proposed. This paper studies how stronger parity reasoning techniques in the DPLL(XOR) framework can be simulated by simpler systems: resolution, unit propagation, and parity explanations. Such simulations are interesting, for example, for developing the next generation SAT solvers capable of handling parity constraints efficiently.
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References
Marques-Silva, J., Lynce, I., Malik, S.: Conflict-driven clause learning SAT solvers. In: Handbook of Satisfiability. IOS Press (2009)
Tseitin, G.S.: On the complexity of derivations in the propositional calculus. Studies in Mathematics and Mathematical Logic Part II, 115–125 (1968)
Urquhart, A.: Hard examples for resolution. Journal of the ACM 34(1), 209–219 (1987)
Pipatsrisawat, K., Darwiche, A.: On the power of clause-learning SAT solvers as resolution engines. Artificial Intelligence 175(2), 512–525 (2011)
Li, C.M.: Integrating equivalency reasoning into Davis-Putnam procedure. In: Proc. AAAI/IAAI 2000, pp. 291–296. AAAI Press (2000)
Li, C.M.: Equivalency reasoning to solve a class of hard SAT problems. Information Processing Letters 76(1-2), 75–81 (2000)
Baumgartner, P., Massacci, F.: The taming of the (X)OR. In: Palamidessi, C., et al. (eds.) CL 2000. LNCS (LNAI), vol. 1861, pp. 508–522. Springer, Heidelberg (2000)
Li, C.M.: Equivalent literal propagation in the DLL procedure. Discrete Applied Mathematics 130(2), 251–276 (2003)
Heule, M., van Maaren, H.: Aligning CNF- and equivalence-reasoning. In: Hoos, H.H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, pp. 145–156. Springer, Heidelberg (2005)
Heule, M., Dufour, M., van Zwieten, J., van Maaren, H.: March_eq: Implementing additional reasoning into an efficient look-ahead SAT solver. In: Hoos, H.H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, pp. 345–359. Springer, Heidelberg (2005)
Chen, J.: Building a hybrid SAT solver via conflict-driven, look-ahead and XOR reasoning techniques. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 298–311. Springer, Heidelberg (2009)
Soos, M., Nohl, K., Castelluccia, C.: Extending SAT solvers to cryptographic problems. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 244–257. Springer, Heidelberg (2009)
Laitinen, T., Junttila, T., Niemelä, I.: Extending clause learning DPLL with parity reasoning. In: Proc. ECAI 2010, pp. 21–26. IOS Press (2010)
Soos, M.: Enhanced gaussian elimination in DPLL-based SAT solvers. In: Pragmatics of SAT, Edinburgh, Scotland, GB, p. 1 (July 2010)
Laitinen, T., Junttila, T., Niemelä, I.: Equivalence class based parity reasoning with DPLL(XOR). In: IEEE Proc. ICTAI 2011, pp. 649–658 (2011)
Laitinen, T., Junttila, T., Niemelä, I.: Conflict-driven XOR-clause learning. In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 383–396. Springer, Heidelberg (2012)
Laitinen, T., Junttila, T., Niemelä, I.: Classifying and propagating parity constraints. In: Milano, M. (ed.) CP 2012. LNCS, vol. 7514, pp. 357–372. Springer, Heidelberg (2012)
Laitinen, T., Junttila, T., Niemelä, I.: Extending clause learning SAT solvers with complete parity reasoning. In: IEEE Proc. ICTAI 2012 (2012)
Weaver, S.A.: Satisfiability advancements enabled by state machines. PhD thesis, Cincinnati, OH, USA, AAI3554401 (2012)
Nieuwenhuis, R., Oliveras, A., Tinelli, C.: Solving SAT and SAT modulo theories: From an abstract Davis-Putnam-Logemann-Loveland procedure to DPLL(T). Journal of the ACM 53(6), 937–977 (2006)
Gwynne, M., Kullmann, O.: On SAT representations of XOR constraints. arXiv document arXiv:1309.3060 (cs.CC) (2013)
Barrett, C., Sebastiani, R., Seshia, S.A., Tinelli, C.: Satisfiability modulo theories. In: Handbook of Satisfiability. IOS Press (2009)
Han, C.-S., Jiang, J.-H.R.: When boolean satisfiability meets gaussian elimination in a simplex way. In: Madhusudan, P., Seshia, S.A. (eds.) CAV 2012. LNCS, vol. 7358, pp. 410–426. Springer, Heidelberg (2012)
Zhang, L., Malik, S.: Validating SAT solvers using an independent resolution-based checker: Practical implementations and other applications. In: IEEE Proc. DATE 2003, pp. 880–885 (2003)
Beame, P., Kautz, H., Sabharwal, A.: Towards understanding and harnessing the potential of clause learning. Journal of Artificial Intelligence Research 22, 319–351 (2004)
Eén, N., Sörensson, N.: An extensible SAT solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 502–518. Springer, Heidelberg (2004)
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Laitinen, T., Junttila, T., Niemelä, I. (2013). Simulating Parity Reasoning. In: McMillan, K., Middeldorp, A., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2013. Lecture Notes in Computer Science, vol 8312. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45221-5_38
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DOI: https://doi.org/10.1007/978-3-642-45221-5_38
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